I love this one.
Basically, the easiest route is in the 40's with the Liberal Leadership accepting the Conservative and National Liberal courtship and merge into Harold Macmillan's proposed 'New Democratic Party', one unified force to oppose Labour.
I'll dig up the specifics, give me a mo.
EDIT: Okay, so after the 1946 Conference, Churchill had a committee set up under the Earl Woolton to get the party back on its feet (this committee included Iain Macleod, Enoch Powell, and Reginald Maudling, then considered the 'brilliant young men' of the Party). Harold Macmillan was also a member of this committee. Taking inspiration from Robert Peel, the Committee decided that a rebrand would be a good solution- scrap the old name and give it a shiny new sexy name that people would vote for. The two that were floated and remembered by history were Harold's 'New Democratic Party', and Woolton's 'Union Party'. Harold and The New Democratic Party are the relevant part of all this.
So October 3rd, 1946, Macmillan published an article in The Telegraph, 'Anti-Socialist Parties Task: The Case for Alliance or Fusion'. Basically the nuts and bolts are that, due to the damage that Socialism was doing to the country, the Conservatives and Liberals, as the two largest 'anti-socialist' Parties, needed to form a united front against Labour under the New Democratic banner, either as an electoral alliance (like the SDP/Liberals years later), or as a straight up new Party (like the Liberal Democrats years later). This came to nothing, large in part thanks to angry Tories who saw through Macmillan (who infamously was in the 30's pushing for a 'Centre Party' on the principles of Social Democracy, preferably to be led by Herbert Morrison, whom he admired greatly until 1945) and the others as neo-socialists (the Post-War consensus and all that).
None the less, Macmillan wasn't put off, and still promoted this 'unified front' through the rest of the 40's and into the 50's, writing after the 1950 Leicester by-election that he would be willing and happy to give the Liberals their long-time policy of PR in exchange for an alliance or merger (PR for big cities; "How else can we eat away at these great Socialist blocs?").
(Macmillan: 1889-1956, page 298-300)
So Macmillan wanted to unite the two parties under Butskellism, which is important. Another thing that is importnt is that, in May 1947, the National Liberal Party and the Conservative Party merged under the Woolton-Teviot Pact agreement. James Henderson-Stewart had, however, failed to convince the Liberal Party to join, writing in a letter to the times ("Outlook For Liberals") that the Liberals should stand against Socialism and join the Conservatives. It wasn't convincing, and it only made a bitter split more bitter. Earlier that same year, he had tried Unifying the National Liberal and Liberal Party, which failed due to the Liberals hatred of the Nats, the Libs seeing them as nothing more than their brand image being misappropriated by the Tories. So he Nats merged with the Tories, which didn't help all that much.
Had Henderson-Stewart been successful in merging the National Liberals and Liberals back together pre-Conservative merger, I believe that Macmillan's proposed Electoral Alliance would have been feasible, and the Liberals may have folded into the Conservatives some years down the line as the New Democratic. Perhaps getting Churchill out of the way would have helped, and having Butler or Macmillan himself lead during the 50's.
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Alternatively, this caught my eye on Wikipeida:
"In 1951 it was only thanks to fraught local arrangements that five of the six remaining Liberal MPs were elected in the absence of a Conservative candidate."
Change those arrangements, and only have one Liberal, and the Party may never escape the nadir.